This is a version of Tom Yam Goong, a popular Thai soup, from the Bangkok and Central Plains region of Thailand. Each region of Thailand has its own individual variation of this recipe. This one uses a black chili paste, which, in my opinion, is the most spicy of all Thai chili pastes (red, green, yellow). Using one of my 20-year-old cookbooks as a guide, I've adapted and enjoyed both recipes over the years.
Shell and remove heads from shrimps. Rinse shells and heads and place them in a large pot with the water. Heat to boiling, then lower heat and bring broth to a very low simmer. Place the shelled shrimps in the fridge until about 5-10 minutes before you're ready to add to the soup.
Trim the lemongrass of its outer sheath and hard ends. Whack it in a few places with a mallet (or back of a knife), then cut into 2 or 3 pieces.
In a medium saucepan, combine the oil, shallots, and garlic and turn heat to medium. Stir for a minute. Add the lemongrass, black chili paste, ginger (or galangal), and lime leaves. Cook for about 3-4 minutes, then add the shrimp broth. Reduce heat to medium and cook at a moderate simmer for 15-20 minutes. Add the fish sauce and mushrooms and cook gently for about 2 minutes. Remove shrimp from the fridge and add to the soup. Reheat to boiling, or until shrimp are cooked through. Add lime juice (and bean sprouts, if using) to soup. Pour soup into bowls, dividing shrimps evenly into each one. Garnish with chopped cilantro and serve.* Serves 4 as an appetizer or 2 as a main course.
*Additional black chili paste, fish sauce, and lime juice could be served as a side in individual bowls.